// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_NUMTRAITS_H
#define EIGEN_NUMTRAITS_H

namespace Eigen {

namespace internal {

// default implementation of digits10(), based on numeric_limits if specialized,
// 0 for integer types, and log10(epsilon()) otherwise.
template<typename T,
		 bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
		 bool is_integer = NumTraits<T>::IsInteger>
struct default_digits10_impl
{
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return std::numeric_limits<T>::digits10; }
};

template<typename T>
struct default_digits10_impl<T, false, false> // Floating point
{
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run()
	{
		using std::ceil;
		using std::log10;
		typedef typename NumTraits<T>::Real Real;
		return int(ceil(-log10(NumTraits<Real>::epsilon())));
	}
};

template<typename T>
struct default_digits10_impl<T, false, true> // Integer
{
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return 0; }
};

// default implementation of digits(), based on numeric_limits if specialized,
// 0 for integer types, and log2(epsilon()) otherwise.
template<typename T,
		 bool use_numeric_limits = std::numeric_limits<T>::is_specialized,
		 bool is_integer = NumTraits<T>::IsInteger>
struct default_digits_impl
{
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return std::numeric_limits<T>::digits; }
};

template<typename T>
struct default_digits_impl<T, false, false> // Floating point
{
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run()
	{
		using std::ceil;
		using std::log;
		typedef typename NumTraits<T>::Real Real;
		return int(ceil(-log(NumTraits<Real>::epsilon()) / log(static_cast<Real>(2))));
	}
};

template<typename T>
struct default_digits_impl<T, false, true> // Integer
{
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static int run() { return 0; }
};

} // end namespace internal

namespace numext {
/** \internal bit-wise cast without changing the underlying bit representation. */

// TODO: Replace by std::bit_cast (available in C++20)
template<typename Tgt, typename Src>
EIGEN_STRONG_INLINE EIGEN_DEVICE_FUNC Tgt
bit_cast(const Src& src)
{
#if EIGEN_HAS_TYPE_TRAITS
	// The behaviour of memcpy is not specified for non-trivially copyable types
	EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Src>::value, THIS_TYPE_IS_NOT_SUPPORTED);
	EIGEN_STATIC_ASSERT(std::is_trivially_copyable<Tgt>::value && std::is_default_constructible<Tgt>::value,
						THIS_TYPE_IS_NOT_SUPPORTED);
#endif

	EIGEN_STATIC_ASSERT(sizeof(Src) == sizeof(Tgt), THIS_TYPE_IS_NOT_SUPPORTED);
	Tgt tgt;
	EIGEN_USING_STD(memcpy)
	memcpy(&tgt, &src, sizeof(Tgt));
	return tgt;
}
} // namespace numext

/** \class NumTraits
 * \ingroup Core_Module
 *
 * \brief Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
 *
 * \tparam T the numeric type at hand
 *
 * This class stores enums, typedefs and static methods giving information about a numeric type.
 *
 * The provided data consists of:
 * \li A typedef \c Real, giving the "real part" type of \a T. If \a T is already real,
 *     then \c Real is just a typedef to \a T. If \a T is \c std::complex<U> then \c Real
 *     is a typedef to \a U.
 * \li A typedef \c NonInteger, giving the type that should be used for operations producing non-integral values,
 *     such as quotients, square roots, etc. If \a T is a floating-point type, then this typedef just gives
 *     \a T again. Note however that many Eigen functions such as internal::sqrt simply refuse to
 *     take integers. Outside of a few cases, Eigen doesn't do automatic type promotion. Thus, this typedef is
 *     only intended as a helper for code that needs to explicitly promote types.
 * \li A typedef \c Literal giving the type to use for numeric literals such as "2" or "0.5". For instance, for \c
 * std::complex<U>, Literal is defined as \c U. Of course, this type must be fully compatible with \a T. In doubt, just
 * use \a T here. \li A typedef \a Nested giving the type to use to nest a value inside of the expression tree. If you
 * don't know what this means, just use \a T here. \li An enum value \a IsComplex. It is equal to 1 if \a T is a \c
 * std::complex type, and to 0 otherwise. \li An enum value \a IsInteger. It is equal to \c 1 if \a T is an integer type
 * such as \c int, and to \c 0 otherwise. \li Enum values ReadCost, AddCost and MulCost representing a rough estimate of
 * the number of CPU cycles needed to by move / add / mul instructions respectively, assuming the data is already stored
 * in CPU registers. Stay vague here. No need to do architecture-specific stuff. If you don't know what this means, just
 * use \c Eigen::HugeCost. \li An enum value \a IsSigned. It is equal to \c 1 if \a T is a signed type and to 0 if \a T
 * is unsigned. \li An enum value \a RequireInitialization. It is equal to \c 1 if the constructor of the numeric type
 * \a T must be called, and to 0 if it is safe not to call it. Default is 0 if \a T is an arithmetic type, and 1
 * otherwise. \li An epsilon() function which, unlike <a
 * href="http://en.cppreference.com/w/cpp/types/numeric_limits/epsilon">std::numeric_limits::epsilon()</a>, it returns a
 * \a Real instead of a \a T. \li A dummy_precision() function returning a weak epsilon value. It is mainly used as a
 * default value by the fuzzy comparison operators. \li highest() and lowest() functions returning the highest and
 * lowest possible values respectively. \li digits() function returning the number of radix digits (non-sign digits for
 * integers, mantissa for floating-point). This is the analogue of <a
 * href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits">std::numeric_limits<T>::digits</a> which is used
 * as the default implementation if specialized. \li digits10() function returning the number of decimal digits that can
 * be represented without change. This is the analogue of <a
 * href="http://en.cppreference.com/w/cpp/types/numeric_limits/digits10">std::numeric_limits<T>::digits10</a> which is
 * used as the default implementation if specialized. \li min_exponent() and max_exponent() functions returning the
 * highest and lowest possible values, respectively, such that the radix raised to the power exponent-1 is a normalized
 * floating-point number.  These are equivalent to <a
 * href="http://en.cppreference.com/w/cpp/types/numeric_limits/min_exponent">std::numeric_limits<T>::min_exponent</a>/
 *     <a
 * href="http://en.cppreference.com/w/cpp/types/numeric_limits/max_exponent">std::numeric_limits<T>::max_exponent</a>.
 * \li infinity() function returning a representation of positive infinity, if available.
 * \li quiet_NaN function returning a non-signaling "not-a-number", if available.
 */

template<typename T>
struct GenericNumTraits
{
	enum
	{
		IsInteger = std::numeric_limits<T>::is_integer,
		IsSigned = std::numeric_limits<T>::is_signed,
		IsComplex = 0,
		RequireInitialization = internal::is_arithmetic<T>::value ? 0 : 1,
		ReadCost = 1,
		AddCost = 1,
		MulCost = 1
	};

	typedef T Real;
	typedef typename internal::
		conditional<IsInteger, typename internal::conditional<sizeof(T) <= 2, float, double>::type, T>::type NonInteger;
	typedef T Nested;
	typedef T Literal;

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real epsilon() { return numext::numeric_limits<T>::epsilon(); }

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int digits10() { return internal::default_digits10_impl<T>::run(); }

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int digits() { return internal::default_digits_impl<T>::run(); }

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int min_exponent()
	{
		return numext::numeric_limits<T>::min_exponent;
	}

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int max_exponent()
	{
		return numext::numeric_limits<T>::max_exponent;
	}

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real dummy_precision()
	{
		// make sure to override this for floating-point types
		return Real(0);
	}

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T highest() { return (numext::numeric_limits<T>::max)(); }

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T lowest()
	{
		return IsInteger ? (numext::numeric_limits<T>::min)() : static_cast<T>(-(numext::numeric_limits<T>::max)());
	}

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T infinity() { return numext::numeric_limits<T>::infinity(); }

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline T quiet_NaN() { return numext::numeric_limits<T>::quiet_NaN(); }
};

template<typename T>
struct NumTraits : GenericNumTraits<T>
{};

template<>
struct NumTraits<float> : GenericNumTraits<float>
{
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline float dummy_precision() { return 1e-5f; }
};

template<>
struct NumTraits<double> : GenericNumTraits<double>
{
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline double dummy_precision() { return 1e-12; }
};

template<>
struct NumTraits<long double> : GenericNumTraits<long double>
{
	EIGEN_CONSTEXPR
	static inline long double dummy_precision() { return 1e-15l; }
};

template<typename _Real>
struct NumTraits<std::complex<_Real>> : GenericNumTraits<std::complex<_Real>>
{
	typedef _Real Real;
	typedef typename NumTraits<_Real>::Literal Literal;
	enum
	{
		IsComplex = 1,
		RequireInitialization = NumTraits<_Real>::RequireInitialization,
		ReadCost = 2 * NumTraits<_Real>::ReadCost,
		AddCost = 2 * NumTraits<Real>::AddCost,
		MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost
	};

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real epsilon() { return NumTraits<Real>::epsilon(); }
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline Real dummy_precision()
	{
		return NumTraits<Real>::dummy_precision();
	}
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline int digits10() { return NumTraits<Real>::digits10(); }
};

template<typename Scalar, int Rows, int Cols, int Options, int MaxRows, int MaxCols>
struct NumTraits<Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols>>
{
	typedef Array<Scalar, Rows, Cols, Options, MaxRows, MaxCols> ArrayType;
	typedef typename NumTraits<Scalar>::Real RealScalar;
	typedef Array<RealScalar, Rows, Cols, Options, MaxRows, MaxCols> Real;
	typedef typename NumTraits<Scalar>::NonInteger NonIntegerScalar;
	typedef Array<NonIntegerScalar, Rows, Cols, Options, MaxRows, MaxCols> NonInteger;
	typedef ArrayType& Nested;
	typedef typename NumTraits<Scalar>::Literal Literal;

	enum
	{
		IsComplex = NumTraits<Scalar>::IsComplex,
		IsInteger = NumTraits<Scalar>::IsInteger,
		IsSigned = NumTraits<Scalar>::IsSigned,
		RequireInitialization = 1,
		ReadCost = ArrayType::SizeAtCompileTime == Dynamic
					   ? HugeCost
					   : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::ReadCost),
		AddCost = ArrayType::SizeAtCompileTime == Dynamic
					  ? HugeCost
					  : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::AddCost),
		MulCost = ArrayType::SizeAtCompileTime == Dynamic
					  ? HugeCost
					  : ArrayType::SizeAtCompileTime * int(NumTraits<Scalar>::MulCost)
	};

	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline RealScalar epsilon() { return NumTraits<RealScalar>::epsilon(); }
	EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR static inline RealScalar dummy_precision()
	{
		return NumTraits<RealScalar>::dummy_precision();
	}

	EIGEN_CONSTEXPR
	static inline int digits10() { return NumTraits<Scalar>::digits10(); }
};

template<>
struct NumTraits<std::string> : GenericNumTraits<std::string>
{
	enum
	{
		RequireInitialization = 1,
		ReadCost = HugeCost,
		AddCost = HugeCost,
		MulCost = HugeCost
	};

	EIGEN_CONSTEXPR
	static inline int digits10() { return 0; }

  private:
	static inline std::string epsilon();
	static inline std::string dummy_precision();
	static inline std::string lowest();
	static inline std::string highest();
	static inline std::string infinity();
	static inline std::string quiet_NaN();
};

// Empty specialization for void to allow template specialization based on NumTraits<T>::Real with T==void and SFINAE.
template<>
struct NumTraits<void>
{};

template<>
struct NumTraits<bool> : GenericNumTraits<bool>
{};

} // end namespace Eigen

#endif // EIGEN_NUMTRAITS_H
